And who knows? Ayane could've dyed her hair at a young age, or is it her official true hair color?
Of course, but lacking of different infos it's just logical to suppose that the most likely explanation it's also the right one, otherwise it should be legit to doubt about everything.
Ayane was showned us purple since like a child so it's very unlikely that a similar person could dye her hair, more living in an old ninja village with old traditions and far from the modern society surely avoid that such behaviors are only taken in consideration from the ones that lives there. For these reasons seems to me just clear that all the ninja that we see (Ayane and Raidou included) never did something similar. Honoka also being hinted to be the sister of Ayane and keeping a very strange natural hair color further confirms that Ayane is a "true purple" xD
Anyway what you said it's not completely unrelated to the matter: in Asian cultures (but to be fair even in Western ones with different extents) where usually the natural hair color is always dark, to have dyed hair color more lighter is usually synonim of rebellion of young age (something overall related to the few individualism inside certain kinds of society) and often can also be associated to delinquent people. Using as examples anime/manga works, it's not a case that characters as Eikichi Onizuka or Naruto Uzumaki, the first one a thug the second ostracized and brat, are represented with blonde hair. In Bleach this matter is explicitely expressed in the beginning of the work related to the peculiar natural hair color of Ichigo.
I'm pretty sure that the reason behind Ayane getting a purple hair color was just dicated from this reason, only that the designers based their decisions in a fantasy context: with a ninja village involved and with a child considered cursed, a blonde dyed hair become a natural purple one, and even the color of the eyes changes to a overnatural one.
PS: However in favor of your thesis has to be said that Ayane's hobby is the make-up xD